A wavelet coefficient *x* is said to be insignificant
with respect to a given threshold *T* if |*x*|<*T*. The
zerotree is based on the hypothesis that if a wavelet
coefficient at a coarse scale is insignificant with respect to
a threshold, then all wavelet coefficients of the
same orientation in the same spatial location at the finer
scale are likely to be insignificant with respect to
the same threshold. More specifically,
in a hierarchical subband system,
with the exception of the highest frequency subbands,
ever coefficient at a given scale can be related to a set
of coefficients at the next finer scale of similar orientation.
The coefficient at the coarse scale is called the *parent, *and
all coefficients corresponding to the same spatial
location at the next finer scale of similar orientation
are called *children. *Similar, we can define the concepts
*descendants *and *ancestors.*The data structure of the zerotree can be visualized in
Figure .
Given a threshold *T* to determine whether or not
a coefficient is significant, a coefficient *x* is said to be an
element of a *zerotree *for the threshold *T* if itself and
all of its descendents are insignificant with respect to the threshold *T*.
Therefore, given a threshold, any wavelet coefficient could be represented
in one of the four data
types: zerotree root (ZRT), isolated zero (IZ)
(it is insignificant but its descendant is not),
positive significant (POS) and negative significant (NEG).